The interval-valued kernel PCA (UQ-KPCA) is a variation of the kernel PCA (KPCA) designed for interval-valued data, designed to handle data uncertainty by defining specific similarity measures and kernel functions for interval data. This paper introduces Uncertainty Quantification KPCA (UQ-KPCA) as a novel method to address uncertainties in data. UQ-KPCA converts the traditional KPCA model from single-valued to interval-valued representations, allowing for accurate error and uncertainty quantification. The process modeling using KPCA is then performed on data based on the interval model, followed by the computation of fault detection statistics such as T2, Q, and Φ. The method’s effectiveness is evaluated in the context of the cement rotary kiln process, and compared with the KPCA demonstrating superior performance in accurately identifying faults within a stochastic setting with unknown uncertainties.

This study introduces three novel dynamic interval-valued principal component analysis (DIPCA) methods: dynamic centers PCA (D-CPCA), dynamic vertices PCA (D-VPCA), and dynamic complete information PCA (D-CIPCA). These methods advance traditional interval-valued PCA (IPCA) by integrating dynamic aspects of industrial processes, thus addressing both data uncertainties and temporal correlations. The DIPCA methods were validated using real-world data from the Ain El Kebira cement plant. Results indicate significant improvements in fault detection accuracy, achieving lower false alarm rates and higher reliability compared to classical IPCA methods. Furthermore, an enhanced combined index for interval-valued data was developed, providing a single, comprehensive statistical measure for streamlined process monitoring.

In this paper, we develop an improved fault detection (FD) technique in order to enhance monitoring abilities of nonlinear chemical processes. Kernel principal component analysis (KPCA) is an effective data driven technique for monitoring nonlinear processes. However, it is well known that data collected from complex and multivariate processes are multiscale due to the variety of changes that could occur in process with different localization in time and frequency. Thus, to enhance process monitoring abilities, we propose to combine advantages of KPCA and multiscale representation using wavelets by constructing a multiscale KPCA model and a new detection chart named multiscale kernel generalized likelihood ratio test (MS-KGLRT) is derived for fault detection. The detection performance of the new chart is studied using the Tennessee Eastman process (TEP).

Fault detection of nonlinear processes using Kernel Principal Component Analysis(KPCA) method has recently prompt a lot of interest due to its industrial practical importance. However, this method cannot be applied for data sets with a large amount of samples. To overcome this deficiency, this paper proposes a reduced KPCA method based on K-means clustering. This method aims to find a reduced data set among the training data in the input space and uses this reduced data set to built the reduced KPCA model in the feature space. The relevance of the proposed method is illustrated on an air quality monitoring network. The simulation results demonstrate the effectiveness of the new method when compared to the classical KPCA technique.

We present in this paper a subspace approach for enhancing a noisy speech signal. The original algorithm for model identification from which we have derived our method has been used in the field of fault detection and diagnosis. This algorithm is based on principal component analysis in which the optimal subspace selection is provided by a variance of the reconstruction error (VRE) criterion. This choice overcomes many limitations encountered with other selection criteria, like overestimation of the signal subspace or the need for empirical parameters. We have also extended our subspace algorithm to take into account the case of colored and babble noise. The performance evaluation, which is made on the Aurora database shows that our method provides a higher noise reduction and a lower signal distortion than existing enhancement methods. Our algorithm succeeds in enhancing the noisy speech in all noisy conditions without introducing artifacts such as “musical noise”. Index Terms: speech enhancement, model identification, signal subspace, principal component analysis, colored noise