A Robust Probabilistic Quality-Relevant Monitoring Model With Laplace Distribution

The historical data collected from industrial processes are generally disturbed by ambient noise and outliers. Hence, accurate estimation of process uncertainty is essential in order to correctly determine the status of the process systems. In this study, a robust probabilistic quality-relevant monitoring model with a Laplace distribution is proposed for industrial process monitoring under noisy environment. Because of the heavy tailed characteristic of Laplace distribution, the proposed model is more robust than models with Gaussian distribution. The solution of the proposed probabilistic model is provided through variational Bayesian inference and maximum likelihood estimation after recasting Laplace distribution as Gaussian scale mixtures. Based on the obtained model parameters and estimated latent variables, a quality-relevant monitoring model can be established and four statistics are designed. According to the calculated statistics, the proposed method can effectively detect and differentiate quality-relevant from quality-independent faults. The performance of the proposed method is illustrated using a numerical simulation and a condenser application, which are disturbed by ambient noise and outliers. Experimental results demonstrate that Laplace distribution can better reveal the process uncertainty to effectively alleviate their negative effect. As a result, the proposed method performs better than some commonly used quality-relevant monitoring strategies.