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When new fault occurs, the parameters and structure of fault diagnosis model based on deep learning need to be adjusted for retraining, which is often very time-consuming. For the above problem, a latent representation dual manifold regularization broad learning system (LRDMR-BLS) with incremental learning capability is proposed for process fault diagnosis. This model embeds latent representation learning into feature selection and utilizes the link information between data to guide feature selection. Meanwhile, manifold regularization is introduced in the objective function to preserve the local manifold structure of the original data space. Further, a manifold regularization term is added to the objective function of the broad learning system to preserve the local structure of the features. Finally, the incremental learning capability of the proposed model is given, which enables the proposed model can be updated quickly when new fault occurs. The superiority of the proposed model is demonstrated by two Chemical processes.

If the three-dimension data of batch process are unfolded the two-dimension data, some important information would lose, and outliers such as noise would lead to poor monitoring results. Therefore, a Markov chain neighborhood sparse preserving graph embedding algorithm based on tensor factorization (TMNSPGE) is proposed. Firstly, tensor factorization is used to directly process the three-dimension data in batch process, which can avoid the information loss. Secondly, by using the neighborhood preserving embedding algorithm and sparse manifold coding, the local linear relationship and local sparse manifold structure of data are preserved. On this basis, Markov chain analysis is introduced to construct a similar graph to make the data after dimensionality reduction have a certain probability interpretation. Finally, the statistics and control limits are determined to realize process monitoring. Numerical example and penicillin fermentation simulation process prove the effectiveness of TMNSPGE algorithm in batch process monitoring. INDEX TERMS Batch process monitoring, finite Markov chain, graph embedding, neighborhood preserving embedding, sparse representation, tensor factorization.

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