A Bayesian inference based two-stage support vector regression framework for soft sensor development in batch bioprocesses

Inherent process and measurement uncertainty has posed a challenging issue on soft sensor development of batch bioprocesses. In this paper, a new soft sensor modeling framework is proposed by integrating Bayesian inference strategy with two-stage support vector regression (SVR) method. The Bayesian inference procedure is first designed to identify measurement biases and misalignments via posterior probabilities. Then the biased input measurements are calibrated through Bayesian estimation and the first-stage SVR model is thus built for output measurement reconciliation. The inferentially calibrated input and output data can be further used to construct the second-stage SVR model, which serves as the main model of soft sensor to predict new output measurements. The Bayesian inference based two-stage support vector regression (BI-SVR) approach is applied to a fed-batch penicillin cultivation process and the obtained soft sensor performance is compared to that of the conventional SVR method. The results from two test cases with different levels of measurement uncertainty show significant improvement of the BI-SVR approach over the regular SVR method in predicting various output measurements. © 2012 Elsevier Ltd. All rights reserved.