Fault Detection Of Batch Process Based On MKICA-PCA

Batch processes widely used in producing small amount and high value-addedproduction, are common modes in modern process industry. The batch processesrepresent strong nonlinearity, dynamic nature and time-variant characteristic.Multivariate statistical techniques are widely used in the batch process monitoring andfault detection at present. Outstanding theories and algorithms are most linearmultivariate statistical model.Process variables can not always satisfy the demand of traditional multivariatestatistical methods that the process variables are Gaussian distribution and linear.Aiming at the batch process which has the nonlinearity and non-Gaussian distributionor mixed distribution, a new monitoring method based on MKICA-PCA is researched.(1) Improvement research of traditional ICA methodExpanding along batches direction and expanding along variables direction aretwo common methods for three-dimensional data of batch process. Expanding alongbatches direction though is the major method, it requests the equal length of everybatch and it has to predict the overall data after the sampling point; expanding alongvariables direction does not sensitive to the faults. A modified expanding method,which take the advantages of two expanding method are used in this paper. Firstexpanding along batches direction and do the standardization, and then expandingalong variables direction to modeling. Meanwhile, through setting threshold value ofnegative entropy is use to achieve the automatically selecting the independent components,which can overcome the shortcoming of predefining the number of independent componentsin traditional method of ICA.(2) Monitoring strategy of MKICA based on KPCA-whiteningThe observation data are usually whitened first before doing the ICA analysis.Kernel principal component analysis is used to do the whitening process. Traditionalwhitening using PCA is a linear transformation based on primitive characters. Kernelprincipal component analysis is a nonlinear method. Its fundamental is making inputspace map into high dimensional feature space, using “kernel technique”, i.e.choosing kernel function and converting the nonlinear problem of input space into the linear condition in feature space. Then PCA method is used to do the whitening in thehigh dimensional space.(3) Research on a monitoring method of MKICA-PCA aiming at the batchprocesses with data mixed distributionProcess variables can not always satisfy the demand of traditional multivariatestatistical methods that the process variables are Gaussian distribution and linear.Thus, based on the foregoing research, a new monitoring method based onMKICA-PCA is researched aiming at the batch process which has the nonlinearityand non-Gaussian distribution or mixed distribution.Process data is mapped into high dimensional linear space and processinformation of non-Gaussian is extracted first using the MKICA method based onKPCA whitening. Setting threshold value of negative entropy is used to achieve theautomatically selecting the independent components, which can overcome theshortcoming of predefining the number of independent components in traditionalmethod of ICA. The confidence limits of the corresponding monitoring statistics aredetermined using kernel density estimation; then the process residual information,which is multivariate Gaussian distribution are further analyzed and processed usingPCA.