Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.

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.

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a b s t r a c t a r t i c l e i n f oTraditional kernel principal component analysis (KPCA) concentrates on the global structure analysis of data sets but omits the local information which is also important for process monitoring and fault diagnosis. In this paper, a modified KPCA, referred to as the local KPCA (LKPCA), is proposed based on local structure analysis for nonlinear process fault diagnosis. In order to extract data feature better, local structure analysis is integrated within the KPCA, and this results in a new optimisation objective which naturally involves both global and local structure information. With the application of usual kernel trick, the optimisation problem is transformed into a generalised eigenvalue decomposition on the kernel matrix. For the purpose of fault detection, two monitoring statistics, known as the T 2 and Q statistics, are built based on the LKPCA model and confidence limit is computed by kernel density estimation. In order to identify fault variables, contribution plots for monitoring statistics are constructed based on the idea of sensitivity analysis to locate the fault variables. Simulation using the Tennessee Eastman benchmark process shows that the proposed method outperforms the traditional KPCA, in terms of fault detection performance. The results obtained also demonstrate the potential of the proposed fault identification approach.

Rainfall-triggered shallow landslides are widespread natural hazards around the world, causing many damages to human lives and property. In this study, we focused on predicting landslides in a large region by coupling a 1 kmresolution hydrological model and a 90 m-resolution slope stability model, where a downscaling method for soil moisture via topographic wetness index was applied. The modeled hydrological processes show generally good agreements with the observed discharges: relative biases and correlation coefficients at three validation stations are all <20% and >0.60, respectively. The derived scaling law for soil moisture allows for near-conservative downscaling of the original 1-km soil moisture to 90-m resolution for slope stability assessment. For landslide prediction, the global accuracy and true positive rate are 97.2% and 66.9%, respectively. This study provides an effective and computationally efficient coupling method to predict landslides over large regions in which finescale topographical information is incorporated.