Hierarchical Canonical Correlation Analysis With Application to Process Monitoring

The idea of stacking layers is adopted to construct a deep multivariate statistical model, hierarchical canonical correlation analysis (HCCA). Its hierarchical structure is motivated form the deep network. The proposed HCCA model has the features of low computational complexity, strong correlative feature extraction, and causal interpretability. Its correlation advantages are theoretically demonstrated, then the evaluation metrics about accuracy and complexity are presented. The HCCA-based fault monitoring method is proposed for industrial processes, and the variable contributions are analyzed based on the residual statistic. The experiment results on Tennessee Eastman and real industry wastewater treatment processes show an average fault detection rate of 87.91<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> and 99.49<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>. It also decreases an average false alarm rate to 0.92<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> and 0.32<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>, respectively.