In order to sustain safety and high product quality, the data-driven fault detection tools are increasingly used in industrial processes. The quality variables are the key index of the final product. Obtaining them in high frequency is time-consuming in the laboratory because they require the efforts of experienced operators. Meanwhile, process variables such as the temperature, the pressure, and the flow rate can be readily sampled in high frequency; hence the sample size between the process and the quality data is quite unequal. To effectively integrate two different observation sources, the high-rate process measurements and low-rate quality measurements, a semi-supervised regression model with probabilistic latent variables is proposed in this article to enhance the performance monitoring of the variations of the process and the quality variables. The corresponding statistics are also systematically developed and a TE benchmark problem is presented to illustrate the effectiveness of the proposed method.
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