A sparse regularized soft sensor based on GRU and self-interpretation double nonnegative garrote: From variable selection to structure optimization

Soft sensors, as a significant paradigm for industrial intelligence, are extensively utilized in large-scale industrial integration systems to estimate the pivotal quality variables. For deep neural network-based soft sensors, redundancy in input variables and network structure has emerged as one of the most important challenges. In this article, a sparse regularized soft sensor based on the gated recurrent unit (GRU) and self- interpretation dual nonnegative garrote is proposed. Initially, a proficiently trained GRU network is established as the pre-trained model, followed by the design of a set of self-interpretation factors based on the mean influence value of different input variables. Secondly, the contraction coefficients of the nonnegative garrote are sequentially incorporated into the GRU input and hidden layer weight matrices. Meanwhile, the self- interpretation factors are introduced into the constraints of the nonnegative garrote algorithm to guide it to adaptively adjust the applied penalty strength based on the relative importance of different input variables. The strategy integrates variable selection with the model training process to sparsify the network structure and provide self-interpretable variable selection results. Finally, the performance of the developed approach is verified through a practical application in power plant desulfurization systems. The case studies demonstrate that the developed approach for soft sensor modeling outperforms other existing methods and shows promising application prospects. In addition, the validity of the self-interpretable variable selection results is verified via the known mechanism analysis and expert experience.