Cobalt oxalate synthesis process is a nonlinear batch process. However, the lack of online sensors for the quality variable (e.g., average particle size) has become the main obstacle of controlling the process accurately and optimally. An active learning strategy for selecting the informative training data is proposed to improve the soft sensor prediction performance. First, an initial data set which is collected from the process is used to establish an LSSVR soft sensor model. Second, the

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... model prediction error is obtained and the joint probability distribution for the prediction error and input variables can be described through a Gaussian mixture model (GMM). Then, the conditional error variance, which can be calculated from the error GMM, is used to select the representative data which can be added to the initial data set and can improve the current LSSVR model for better performance. In addition, an evaluation index is presented to implement the active learning procedure. Finally, the proposed method applicability to an industrial cobalt oxalate synthesis process is demonstrated. INDEX TERMS Active learning, cobalt oxalate synthesis process, Gaussian mixture model, least squares support vector regression, soft sensor. 40810 2169-3536