Multiway kernel independent component analysis based on feature samples for batch process monitoring

Abstract

a b s t r a c tMost batch processes generally exhibit the characteristics of nonlinear variation. In this paper, a nonlinear monitoring technique is proposed using a multiway kernel independent component analysis based on feature samples (FS-MKICA). This approach first unfolds the three-way dataset of a batch process into the two-way one and then chooses representative feature samples from the large two-way input training dataset. The nonlinear feature space abstracted from the unfolded two-way data space is then transformed into a high-dimensional linear space via kernel function and an independent component analysis (ICA) model is established in the mapped linear space. The proposed FS-MKICA method can significantly reduce the computational cost in extracting the kernel ICA model since it is based on the small subset of feature samples rather than on the entire input sample set. We supply two statistics, the I 2 statistic of process variation and the squared prediction error statistic of residual, for on-line monitoring of batch processes. The proposed method is applied to detecting faults in the fed-batch penicillin fermentation process. The standard linear ICA method for batch process monitoring, known as the multiway independent component analysis (MICA), is also applied to the same benchmark batch process. The simulation results obtained in this nonlinear batch process application clearly demonstrate the power and superiority of the new nonlinear monitoring method over the linear one. The FS-MKICA approach can extract the nonlinear features of the batch process while the MICA method cannot.

Monitoring Nonlinear and Non-Gaussian Processes Using Gaussian Mixture Model-Based Weighted Kernel Independent Component Analysis

“…To conduct fault detection based on the extracted KICs by KICA, two monitoring statistics are constructed [4], [14], [23]:…”

“…For the WKICAbased method, additionally the weights used in W I 2 t and W Q t need to be determined on-line based on (23). Since the values of standard Gaussian CDF are calculated off line and stored in the memory space, the on-line computing of the probabilities f i (s i,t ) for 1 ≤ i ≤ a becomes retrieving the values from the memory, which is extremely fast.…”

“…Fan et al [22] proposed a filtering KICA-PCA method to improve the process monitoring performance, which applies genetic algorithm to determine the kernel parameter and adopts the exponentially weighted moving average technique to filter the monitoring statistics. To solve the monitoring problem of nonlinear batch processes, Tian et al [23] proposed a multiway KICA method, which unfolds the three-way dataset into the two-way one and then selects representative feature samples to construct the KICA monitoring model.…”

Modified kernel principal component analysis based on local structure analysis and its application to nonlinear process fault diagnosis

“…In order to analyse multiscale data, multi-scale KPCA methods were studied by combining the wavelet analysis and ensemble empirical mode decomposition [13][14][15][16]. To improve the computation efficiency, Tian et al [17] and Cui et al [18] used feature sample selection to reduce the computational complexity of calculating the kernel matrix in KPCA. Nguyen and Golinval [19] applied the KPCA to detect mechanical system faults by comparing the subspace angle between a reference and the current state.…”

A Character of Rotating Machinery Defined Based on KICA

“…The approach is more robust than other ICA algorithms with regards to variations in source densities, degree of non-Gaussianity, and presence of outliers. So it is particularly appropriate in situations where little is known about the underlying sources [5][6][7]. This research aims at defining a character of rotating machinery--KIC, that the typical rolling bearing and gear failure modes can be effectively identified by using the character.…”