Real-time estimation of quality-related variable for dynamic and non-Gaussian process based on semisupervised Bayesian HMM

Real-time sensing of product quality-related key variables in industrial processes has long been a tough task due to technical or economical limitations. Data-driven soft sensing techniques prove to be promising solution to this problem. However, industrial data are complicated with compound complex characteristics, in particular the intractable process dynamics, non-Gaussian distributions and missing value of the quality variables, which render significant difficulties in the development of high-accuracy soft sensor. Given such vexed issues, this paper proposes a dynamic soft sensing method called ‘semisupervised Bayesian hidden Markov model (SsBHMM)’. In the SsBHMM, a semisupervised fully Bayesian regressive model structure is first designed, which accounts for the process dynamics using first-order Markov chain with hidden variables (HVs) and deals with the non-Gaussianities by mixture of Gaussians. Moreover, based on variational inference an efficient training algorithm is developed to learn parameters of the SsBHMM, which mines both labeled and unlabeled data such that the issue of missing value of quality variables can be dealt with. The performance of the SsBHMM is evaluated by a numerical example and an industrial low-temperature transformation unit, through which the advantages and the feasibility of the SsBHMM have been demonstrated. • A novel soft sensor model ’SsBHMM’ for non-Gaussian and dynamic process is proposed. • A semisupervised efficient learning algorithm is developed to train the SsBHMM. • Promising application foreground of the SsBHMM is demonstrated for practitioners.