Soft sensor development based on kernel dynamic time warping and a relevant vector machine for unequal-length batch processes

The unequal-length problem in batch process data directly affects the performance of data-driven soft sensors. Meanwhile, the nonlinearity and high dimensionality of batch process data make the unequal-length problem more serious, and the development of effective soft sensors for unequal-length batch processes has become a challenge. To fully address this challenge, an effective soft sensor based on kernel dynamic time warping and a relevant vector machine is proposed in this paper. The proposed soft sensor consists of trajectory synchronization and online prediction modeling. First, combining the kernel trick, we design a kernel DTW (KerDTW) algorithm to effectively solve the synchronization of unequal-length trajectories with high dimensionality and strong nonlinearity characteristics. Meanwhile, a novel synchronization performance combination index (SPCI) is proposed to realize adaptive selection of the optimal parameter of the KerDTW algorithm. Then, based on the synchronized batch trajectories using the KerDTW algorithm, an online prediction model is established using an RVM to achieve online quality prediction of nonlinear process data. The effectiveness of the proposed soft sensor is illustrated through a penicillin fermentation process.