Deep Learning, Semi-supervised Learning, Soft sensors, Autoencoders, LSTM, Mutual Information.

Deep learning is growing in popularity in virtual sensor modeling problems - the soft sensors - applied to industrial processes of accentuated nonlinearity. Virtual sensors can generate estimates of process variables, which are associated with quality indexes in real- time. Thus, such sensors are a viable alternative when the variables of interest are difficult to measure due to some limiting factor: unavailability of hardware sensors or large measu- rement intervals. Traditional machine learning strategies show difficulties to model such sensors. Typically, industrial processes are highly nonlinear, and the amount of available labeled data is scarce. Due to that, the extraction of representative features present in the abundant amount of unlabeled data has become an area of interest in the development of virtual sensors. From the aforementioned premises, a new virtual sensor modeling tech- nique based on deep learning and representation, which integrates stacked autoencoders (SAE), mutual information (MI), long short-term memory (LSTM), and aggregation bo- otstrap , is proposed. First, in the unsupervised stage, the SAE structure is hierarchically trained layer-by-layer. After a layer’s training, MI analysis is conducted between the tar- get outputs of the model and the representations of the current layer to assess the learned characteristics. The proposed method removes irrelevant information and weights the re- tained ones. The given weights being proportional to the relevance of the representation. Therefore, this approach can extract deep representative information. In the supervised step, called fine-tuning, an LSTM structure is coupled to the tail of the SAE structure to address the intrinsic dynamic behavior of the evaluated industrial systems. Further, a ensemble strategy, called bootstrap aggregation, combines the models obtained in the supervised training phase to improve the performance and credibility of the virtual sen- sor. The proposal uses two industrial nonlinear processes, widely used as benchmarks, to evaluate the performance of the models generated by the proposed technique in the implementation of soft sensors. The results show that the proposed virtual sensors ob- tained better prediction performance than traditional methods and several state-of-the-art methods.