Variable partition based parallel dictionary learning for linearity and nonlinearity coexisting dynamic process monitoring

In practical industrial processes with complex mechanisms, there are both linear and nonlinear relationships between process variables. However, focusing solely on one of these relationships can lead to the neglect of important information related to faults. This neglect can degrade the monitoring performance and increase the potential risk of catastrophic accidents caused by unreliable fault alarms. In order to solve this puzzle, this paper proposes a variable partition based parallel dictionary learning (PDL) method. Firstly, a linearity maximization analysis (LMA) method is presented to recognize linear variable subsets efficiently. The collinearity of variables is evaluated using the variance inflation factor, then linear and nonlinear variable subsets can be divided by maximizing the linear correlation between one variable and the rest. After that, a PDL based monitoring model can be constructed in all subsets to extract linear and nonlinear features concurrently. Finally, based on Bayesian inference, the monitoring results of all subsets are fused to construct a global monitoring statistic. The effectiveness of the proposed approach is illustrated by a numerical simulation case, the continuous stirred tank heater, the Tennessee Eastman process, and a real industrial roasting process. Experiment results show that linear and nonlinear variable subsets can be divided reasonably according to the proposed LMA method. Meanwhile, compared with several state-of-the-art methods, the proposed method can achieve better monitoring results by modeling linear and nonlinear data parts separately, which further demonstrates the feasibility of the proposed method.