Real-time nonlinear multimode process monitoring of actual industrial systems has attracted increasing attention recently. In this article, the time-weighed kernel sparse representation (TWKSR) method is proposed to partition the mode of the training dataset by introducing the time-series-dependent characteristics into the kernel sparse representation algorithm. The alternating direction method of multipliers is utilized to solve the optimization problem of the proposed TWKSR method. Then, the representative samples from each identified mode are selected to update the dictionary matrix. Based on the updated dictionary matrix, the sparse coefficient is used for online mode identification, and the reconstruction error is utilized for fault detection. Finally, a numerical simulation case and the wastewater treatment process example verify the effectiveness of the proposed method.

Motivated by the superior performance of region covariance descriptor, we use covariance matrices as new features to replace the original spectral pixel features, and employ a Log-Euclidean metric to characterize the geodesic distance between symmetric positive definite (SPD) covariance matrices. Based on the covariance features and Log-Euclidean metric, we propose a Log-Euclidean kernel-based joint sparse representation (LogEKJSR) model for the classification of hyperspectral images (HSIs). In the implementation of LogEKJSR, we first reduce the dimensionality of HSI by employing extended multiattribute profile (EMAP) transformations, and then extract the region covariance matrix features associated with each pixel on the EMAPs. The EMAP can model homogeneity and texture structure of HSI by aggregating multiple morphological attribute profiles, the covariance matrix feature contains both local spectral correlation and spatial structure information, and the Log-Euclidean kernel is a matrix-to-matrix similarity metric rather than vector-to-vector similarity metric. Finally, a LogEKJSR model is obtained by replacing the traditional kernel in the KJSR with the Log-Euclidean kernel. Experimental results on three benchmark hyperspectral data sets demonstrate that our proposed LogEKJSR is more effective than existing JSR, KJSR, and support vector machine methods.

This paper proposes a novel unsupervised domain adaption (DA) method called ideal regularized discriminative multiple kernel subspace alignment (IRDMKSA) for hyperspectral image (HSI) classification. The proposed IRDMKSA method includes three main steps: ideal regularization, discriminative multiple kernel learning and subspace alignment. The ideal regularization strategy exploits label information of source domain to refine the standard source and target kernels and also to build a connection between them. The discriminative multiple kernel learning can learn a composite kernel to describe the nonlinearity of HSI samples by fusing complementary information among different single kernels. Finally, the subspace alignment is used to diminish the difference between source and target composite kernels. The proposed IRDMKSA method exploites both the sample similarity and label similarity and makes the resulting kernel more appropriate for DA tasks. Experimental results on five domain adaptation tasks show that the performance of IRDMKSA is better than some classical unsupervised DA methods for the HSI classification.