Multiscale classification has potential advantages for monitoring industrial processes generally driven by events in different time and frequency domains.In this study, we adopt stationary wavelet transform for multiscale analysis and propose an applicable scale selection method to obtain the most discriminative scale features.Then using the multiscale features, we construct two classifiers:(1) a supported vector machine(SVM) classifier based on classification distance, and(2) a Bayes classifier based on probability estimation.For the SVM classifier, we use 4-fold cross-validation and grid-search to obtain the optimal parameters.For the Bayes classifier, we introduce dimension reduction techniques including kernel Fisher discriminant analysis(KFDA) and principal component analysis(PCA) to investigate their influence on classification accuracy.We tested the classifiers with two simulated benchmark processes:the continuous stirred tank reactor(CSTR) process and the Tennessee Eastman(TE) process.We also tested them on a real polypropylene production process.The performance comparison among the classifiers in different scales and scale combinations showed that when datasets present typical scale features, the multiscale classifier had higher classification accuracy than conventional single scale classifiers.We also found that dimension reduction can generally contribute to a better classification in our tests.
Yu-ming LIU Lu-bin YE Ping-you ZHENG Xiang-rong SHI Bin HU Jun LIANG
Abstract Data-driven tools, such as principal component analysis （PCA） and independent component analysis （ICA） have been applied to different benchmarks as process monitoring methods. The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latentvariables are independent. Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution. However, this kind of constraint cannot be satisfied by several practical processes. To ex-tend the use of PCA, a nonparametric method is added to PCA to overcome the difficulty, and kernel density estimation （KDE） is rather a good choice. Though ICA is based on non-Gaussian distribution intormation, .KDE can help in the close monitoring of the data. Methods, such as PCA, ICA, PCA.with .KDE（KPCA）, and ICA with KDE,（KICA）, are demonstrated and. compared by applying them to a practical industnal Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.
In industrial processes,there exist faults that have complex effect on process variables.Complex and simple faults are defined according to their effect dimensions.The conventional approaches based on structured residuals cannot isolate complex faults.This paper presents a multi-level strategy for complex fault isolation.An extraction procedure is employed to reduce the complex faults to simple ones and assign them to several levels.On each level,faults are isolated by their different responses in the structured residuals.Each residual is obtained insensitive to one fault but more sensitive to others.The faults on different levels are verified to have different residual responses and will not be confused.An entire incidence matrix containing residual response characteristics of all faults is obtained,based on which faults can be isolated.The proposed method is applied in the Tennessee Eastman process example,and the effectiveness and advantage are demonstrated.
