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    Enhancing Fault Detection in Stochastic Environments Using Interval-Valued KPCA: A Cement Rotary Kiln Case Study
    (Institute of Electrical and Electronics, 2025) Louifi, Abdelhalim; Kouadri, Abdelmalek; Harkat, Mohamed-Faouzi; Bensmail, Abderazak; Mansouri, Majdi
    Fault detection in industrial processes is challenging due to significant data uncertainty, which complicates the accurate modeling of interval-valued data and the quantification of errors necessary for reliable detection. Existing approaches, such as kernel principal component analysis (KPCA), struggle with these challenges because they rely on single-valued data representations and are unable to effectively handle interval-based variability. To address these limitations, this paper introduces the interval-valued model KPCA (IV-KPCA), which extends KPCA by redefining similarity measures and kernel functions to accommodate interval-valued uncertainty. IV-KPCA preserves the interval structure throughout the modeling process, enhancing robustness to dynamic uncertainties and improving fault detection in complex nonlinear systems. Within this framework, fault detection statistics (T 2 , Q, and 8) are developed to enable precise error quantification. The proposed method is validated on a cement rotary kiln process, a highly stochastic industrial system characterized by significant uncertainties. Experimental results demonstrate that IV-KPCA reduces false alarms, missed detections, and detection delays by over 100%, 90%, and 95%, respectively, compared to traditional methods. These findings underscore the potential of IV-KPCA in enhancing fault detection performance in complex, uncertain environments
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    Sensor Fault Detection in Uncertain Large-Scale Systems Using Interval-Valued PCA Technique
    (IEEE, 2025) Louifi, Abdelhalim; Kouadri, Abdelmalek; Harkat, Mohamed-Faouzi
    Principal component analysis (PCA)-based fault detection and diagnosis (FDD) is a well-established, data- driven method that has shown remarkable performance. Despite the excellent reputation of the PCA, it is not an opti- mal solution, mainly due to the effect of system parameters’ uncertainties and imprecise measurements. These drasti- cally affect the decision-making concerning the operating state of the process. In this article, the data collected by different sensors are transformed from a single value to an interval value form by which errors and uncertainties in the measurements are quantified satisfactorily. Then, the process modeling based on the PCA technique has been duly performed for interval-valued. Afterward, the well-known fault detection statistics T 2 , Q, and 8 are obtained under an interval-valued representation. The developed technique is tested in the cement rotary kiln process. Its performance in terms of false and missed alarms and detection delay is compared with that of other techniques through an actual involuntary system fault and other different types of sensor faults. The obtained results show high superiority in detecting accurately and quickly distinct faults in a stochastic environment, including unknown and uncontrolled uncertainties. Consequently, the results have been reduced by more than 33%, 85%, and 45% for T 2 , Q, and 8, respectively, compared with the best results of the studied methods.
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    Uncertainty Quantification Kernel PCA: Enhancing Fault Detection in Interval-Valued Data
    (Institute of Electrical and Electronics Engineers Inc., 2024) Louifi, Abdelhalim; Kouadri, Abdelmalek; Harkat, Mohamed Faouzi; Bensmail, Abderazak; Mansouri, Majdi; Nounou, Hazem
    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 T 2 , 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.
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    Improving kernel PCA-based algorithm for fault detection in nonlinear industrial process through fractal dimension
    (Institution of Chemical Engineers, 2023) Kaib, Mohammed Tahar Habib; Kouadri, Abdelmalek; Harkat, Mohamed Faouzi; Bensmail, Abderazak; Mansouri, Majdi
    Principal Component Analysis (PCA) is a widely used technique for fault detection and diagnosis. PCA works well when the data set has linear characteristics. However, most industrial processes have nonlinear characteristics in their data. Kernel PCA (KPCA) is an alternative solution for such types of data sets. This solution doesn’t come without a cost since one of KPCA’s disadvantages is a large number of observations which results in more occupied storage space and more execution time than the PCA technique. Furthermore, if the data is too large it may minimize the monitoring performance of the KPCA model. Reduced KPCA (RKPCA) is a solution for the conventional KPCA limitations. Firstly, RKPCA can deal with nonlinear characteristics without crucial problems because it is based on the KPCA algorithm with a data reduction part where it keeps most of the data’s infor- mation. Thus, by reducing the number of observations RKPCA reduces the occupied storage space and execution time while preserving tolerable monitoring performance. The proposed RKPCA algorithm consists of two parts. First, the large-sized training data set is reduced using the fractal dimension technique (correlation dimension). Afterward, the KPCA model is developed through the obtained reduced training data set. The proposed scheme is applied to the Tennessee Eastman Process and the Cement Plant Rotary Kiln data sets to evaluate its performance in comparison with other algorithms.
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    RKPCA-based approach for fault detection in large scale systems using variogram method
    (Elsevier, 2022) Kaib, Mohammed Tahar Habib; Kouadri, Abdelmalek; Harkat, Mohamed Faouzi; Bensmail, Abderazak
    Principal Component Analysis (PCA)-based approach for fault detection is a simple and accurate data-driven technique for feature extraction and selection. However, PCA performs poorly if the data used has nonlinear characteristics where this type of data is widely present in most industrial processes. To overcome this drawback, Kernel PCA (KPCA) is an alternative technique used to work on this type of data but it requires more computation time and memory storage space for large-sized data sets. Many size reduction techniques have been developed to select the most relevant observations that will be employed by KPCA. This, known as Reduced KPCA (RKPCA), consequently requires less computation time and memory storage space than KPCA. Besides, it possesses the advantages of both KPCA and standard PCA. In this paper, a reduction in the size of a data set based on a multivariate variogram is proposed. According to its conventional formalism, the uncorrelated observations are selected and kept to form a reduced training data set. Afterward, the KPCA model is built through this data set for faults detection purposes. The proposed RKPCA scheme is tested using an actual involuntary process fault and various simulated sensor faults in a cement plant. Compared to other RKPCA techniques, the developed one yields better results
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    A modified moving window dynamic PCA with fuzzy logic filter and application to fault detection
    (Elsevier, 2018) Ammiche, Mustapha; Kouadri, Abdelmalek; Bensmail, Abderazak
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    An adaptive threshold estimation scheme for abrupt changes detection algorithm in a cement rotary kiln
    (Elsevier, 2014) Kouadri, Abdelmalek; Bensmail, Abderazak; Kheldoun, Aissa; Refoufi, Larbi