Soft sensor design based on phase partition ensemble of LSSVR models for nonlinear batch processes

Traditional single model based soft sensors may have poor performance on quality prediction for batch processes because of the strong nonlinearity, multiple-phase, and time-varying characteristics. Therefore, a phase partition based ensemble learning framework upon least squares support vector regression (LSSVR) is proposed for soft sensor modeling. Firstly, multiway principal component analysis (MPCA) is employed to handle high-dimensional datasets and extract essential correlation information. Then, different operation phases of the process can be identified by the phase partition strategy based on Gaussian mixture model (GMM) method. Meanwhile, the optimal Gaussian component number is determined by Bayesian information criterion (BIC) technique. Further, multiple localized LSSVR models are constructed to characterize the various dynamic relationships between quality and process variables for local regions, while the grid search (GS) and ten-fold cross-validation methods are introduced to parameter optimization for each local model. Finally, the posterior probability for each test sample with respect to different phases can be estimated by Bayesian inference strategy, and local outputs are integrated to produce the final quality prediction results. Feasibility and superiority of the proposed soft sensor are validated through a case study for penicillin fermentation process. It can achieve satisfactory prediction accuracy and effectively tackle nonlinear and multi-phase modeling problems in chemical and biological processes.