A Monitoring Method Of Unequal Length Batch Processes Based On FVS-BDKPCA

Modern industrial process tend to batch processes gradually that produce low-volume, multi-species and high value-added products. Compared with continuous process, the characteristics of batch process is more complex. The data has the features of multi-stage, nonlinear, dynamic and multi-batch. It is more difficult to monitor the batch process. The monitoring methods based on multivariate statistical process do not require the accurate structural model of process, and the research can be quickly applied to actual industrial processes. As a result, it has been extensively studied, and has become one of hot research of process control field.Batch dynamic kernel principal component analysis (BDKPCA) which has considered the data characteristics of multi-batch, dynamic and nonlinear is better able to apply to batch process. Compared with MKPCA, It is no need to estimate future data when online monitoring, and the accuracy is higher. On the basis of the BDKPCA method, this paper has discussed the choice, of the kernel function and the parameter determination of the kernel function in detail, and has made the SPE statistic of monitoring model approximate the chi-square distribution, get an SPE control limits that has nothing to do with sampling time. In addition, this paper also introduces the idea of sub-period modeling to BDKPCA method, which divide into periods according to the characteristics of the process, and establish a monitoring model for each period that take full account of the different characteristics of different periods.The above method does not take the unequal-length problem into account. For various reasons, the actual industrial process can not be repeated completely. As a result, the length of the data for each batch can not be identical. The paper will introduce feature vector selection (FVS) to BDKPCA, and make improvements for the characteristics of batch process. In the end, the paper will put forward a multivariate statistical monitoring method based on FVS-BDKPCA for batch process. This method is not only effective to solve the problem of unequal-length in batch process, but also reduce the size of the model significantly, making the storage space and computing time reduced effectively when online monitoring. On the basis of this method, the paper also discusses the certainty of the number of feature samples.The core idea of FVS is that using a kernel function to map the original non-linear data to high-dimensional linear space, then selecting some feature samples and using the linear combination of them to represent the entire sample set. However, this method only considers the data of one batch, ignoring other batches. The paper presents a improved FVS method for multiple batches. This method not only considers the similarity between the batch data (data fluctuations caused by random perturbations in the process does not affect the choice of feature samples), but also considers the batch’s characteristics of unequal length. As a result, the selected feature samples of each batch are in similar location and have same number of samples. The method has a good monitoring performance when used in penicillin fermentation process.