Early detection of incipient faults is a challenging task in chemical process monitoring field. As an effective incipient fault detection tool, statistical local kernel principal component analysis (SLKPCA) has demonstrated its advantage over the traditional kernel principal component analysis (KPCA). However, how to improve its incipient fault detection performance is still a valuable problem. In this paper, an enhanced SLKPCA method, referred to as two-dimensional weighted SLKPCA (TWSLKPCA), is proposed by integrating the sample and component weighting strategies. Different to KPCA, SLKPCA monitors the process changes based on the residual vectors computed by the statistical local approach. To highlight the influence of the faulty residual samples, the residual sample weighting strategy is first designed based on the distance between the tested samples and the training samples, which puts large weights on the samples with strong fault information. Furthermore, the residual component weighting strategy is developed to assign large weights to the sensitive components, which are judged by computing the mutual information between the sampleweighted residual components and the original measured variables. Based on the two-dimensional weighted residual vectors, two monitoring statistics are built to detect the incipient faults. Finally, simulations on a numerical example and the Tennessee Eastman process are used to demonstrate the superiority of the proposed TWSLKPCA method.

A non-smooth SIR Filippov system is proposed to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. We synthetically consider both the number of infected population and its changing rate as the switching condition to implement the curing measures. By using the properties of the Lambert W function, we convert the proposed switching condition to a threshold value related to the susceptible population. The classical epidemic model involving media coverage, linear functions describing injecting vaccine and treatment strategies is examined when the susceptible population exceeds the threshold value. In addition, we consider another SIR model accompanied with the vaccination and treatment strategies represented by saturation functions when the susceptible population is smaller than the threshold value. The dynamics of these two subsystems and the sliding domain are discussed in detail. Four types of local sliding bifurcation are investigated, including boundary focus, boundary node, boundary saddle and boundary saddle-node bifurcations. In the meantime, the global bifurcation involving the appearance of limit cycles is examined, including touching bifurcation, homoclinic bifurcation to the pseudo-saddle and crossing bifurcation. Furthermore, the influence of some key parameters related to the three treatment strategies is explored. We also validate our model by the epidemic data sets of A/H1N1 and COVID-19, which can be employed to reveal the effects of media report and existing strategy related to the control of emerging infectious diseases on the variations of confirmed cases.

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Statistical local kernel principal component analysis (SLKPCA) has demonstrated its success in incipient fault detection of nonlinear industrial processes by incorporating the statistical local analysis (SLA) technology. However, the basic SLKPCA method builds the statistical model only based on the normal data and neglects the utilization of the prior fault information, which is often available in many industrial cases. To take full advantage of the prior fault information, this paper proposes an enhanced SLKPCA method, called primary-auxiliary SLKPCA (PA-SLKPCA), for better incipient fault monitoring. The contribution of the proposed method includes three aspects. First, one primary-auxiliary statistical monitoring framework is designed, by which not only the normal training data are applied to develop a primary SLKPCA model, but also the prior fault data are used to build the auxiliary SLKPCA models. Second, a double-block modeling strategy is developed to construct the auxiliary SLKPCA model for each fault case, where a variable grouping strategy based on Kullback-Leibler divergence is applied to divide the process variables into the fault-relevant group and fault-independent variable group, and the sub-model is developed for each group. Third, the Bayesian inference is used to combine the statistical results of each variable group, and one weighted fusion strategy is further designed to integrate the monitoring results from the primary and auxiliary models. Lastly, two case studies including one numerical system and the simulated continuous stirred tank reactor (CSTR) system are used for method evaluation and the simulations show that the proposed method can detect the incipient faults effectively and outperform the traditional SLKPCA method.INDEX TERMS Incipient fault, fault detection, kernel principal component analysis, statistical local analysis, prior fault information.

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