Among a variety of virtual metrology models, dynamic generative latent variable models (DGLVMs) have proven to be an effective tool, owing to outstanding advantages in dealing with complicated data characteristics including temporal correlations, variable colinearities, high dimensionality, and process and measurement uncertainties. Presently, the vast majority of DGLVMs are developed upon the assumption that data are Gaussian-distributed, which is however, non-robust against outlying data and leads the DGLVMs to compromised performance, as the Gaussian distribution is susceptible to outliers that would skew the estimated parameters of DGLVMs. In view of this, this paper proposes a semi-supervised robust learning (SsRL) framework for the DGLVMs by designing an ad-hoc fully robust model structure that handles the outlying data by means of the heavy-tail properties of Student’s t distribution. In addition, the SsRL-DGLVM framework is initiated as a concrete model using probabilistic slow feature analysis (denoted RoSsPSFA) for which a rigorous training algorithm without resorting to any approximations is developed. The performance of the RoSsPSFA is thoroughly evaluated by both numerical and real-world industrial cases, showing the RoSsPSFA’s better immunity against outlying data and higher generalization accuracy.
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