Multirate Mixture Probability Principal Component Analysis for Process Monitoring in Multimode Processes

Abstract

In the multirate sampling processes, the process data are usually collected from various operating conditions and display multimodal characteristics. To monitor these multirate multimode processes, a multirate mixture probability principal component analysis model is proposed for process modeling and fault detection. In this model, the local multirate models are built first for each mode and all of them are subsequently fused with the mixture modeling approach. Such model is able to deal with multirate data with various amount of sampling rates, contributing to a remarkable fault detection and mode identification performance by utilizing all the available measurements even if some variables are unobserved. Then the expectation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula> maximum algorithm is utilized to estimate all the model parameters in the probabilistic framework and the corresponding monitoring method is also developed based on the constructed models. Finally, the effectiveness of the proposed method is demonstrated through a PRONTO benchmark and a real multimode ammonia synthesis process. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Motivated by the practical problem of ununiform sampling intervals in multimode processes, this paper proposes a novel multirate mixture probability principle component analysis model for processes modeling and monitoring. In this model, all the available observations with different sampling rates can be incorporated, which contributes greatly to capturing the multimodal characteristics within the industrial processes. Such ability is the key to realize multimode process monitoring, evaluation, fault diagnosis, and process optimization. In addition, although this paper only focuses on the continuous multirate data in industry, it is equally applicable to other forms of multirate data, such as images and videos.