Hierarchical Key-Historical-Information Transfer Method for Limited-Sample Operating Conditions Monitoring

Industrial processes often operate under multiple operating conditions. Monitoring for unusual modes is a challenge due to the limited availability of samples. In this article, a hierarchical key-historical-information transfer (HkhiT) and subspaces monitoring method is proposed for processes with multiple operating conditions, where historical operating conditions knowledge is transferred hierarchically for limited-sample fault detection. Firstly, a well-conditioned covariance matrix is constructed within the target sample subspace; this procedure mitigates correlation-estimation uncertainty under limited-sample conditions. The principal monitoring subspace then integrates historical correlation information to regularize the target correlation structure. Subsequently, the complementary monitoring subspace extracts latent variables that are sensitive to process disturbances, thereby achieving more comprehensive monitoring of online variations. With limited training data, the decision fusion of the principal and complementary monitoring subspaces provides robust monitoring performance. Finally, the effectiveness of the proposed method is demonstrated through a numerical case and the Tennessee Eastman process.