Dual learning-based online ensemble regression approach for adaptive soft sensor modeling of nonlinear time-varying processes

Soft sensors have been widely used to estimate difficult-to-measure variables in the process industry. However, the nonlinear nature and time-varying behavior of many processes pose significant challenges for accurate quality prediction. Thus a novel adaptive soft sensor, referred to as dual learning-based online ensemble regression (DLOER), is proposed for nonlinear time-varying processes. To deal with process nonlinearity, just-in-time (JIT) learning is used to build local domains and local models simultaneously while statistical hypothesis testing is employed to remove redundant local models. As a result, multiple diverse local models are constructed for characterizing various process states. Then the posterior probabilities of each test sample with respect to different local models are estimated through Bayesian inference and further set as adaptive weights to combine local predictions into a final output. Moreover, DLOER is equipped with incremental local learning and JIT learning for model adaptation, which enables recursive adaptation and online inclusion of local models, respectively. Therefore, process nonlinearity can be well handled under the local learning framework while both gradual and abrupt changes of processes can be efficiently addressed using the dual learning-based adaptation mechanism. The effectiveness of the DLOER approach is demonstrated through a fed-batch penicillin fermentation process.