Orthogonal long short-term memory autoencoder for semi-supervised soft sensor modeling

Data-driven soft sensor methods are popularly applied to predict hard-to-measure variables in industrial production processes. However, in practice, the number of labeled samples is limited, which will affect the accuracy of developed soft sensors. Aiming at this point, semi-supervised soft sensor methods are proposed that combine unsupervised feature extraction and supervised mapping correlation establishment. Auto encoder (AE) is a commonly used feature extraction method for effectively capturing the nonlinear features of processes from unlabeled data. Since typical AEs have no special constraints on the output of latent space, there could be redundancy among the extracted features, which will increase the complexity of mapping correlation establishment. Meanwhile, the dynamic features of processes are difficult to extract by typical AE. Both issues could affect the performance of soft sensors. To address these issues, an Orthogonal Long Short-Term Memory Auto encoder (OLAE) is proposed in this work. By adding the orthogonal constraint on latent space output to the loss function of Long Short-Term Memory Auto encoder, orthogonal dynamic features can be obtained. Then, the OLAE is employed in the feature extraction stage. Using Chatterjee's New Coefficient, orthogonal features related to hard-to-measure variables are screened out for mapping correlation establishment. Considering the limited number of labeled data samples, a prediction model based on support vector regression is established to realize the prediction of hard-to-measure variables. Data from a penicillin fermentation process and an industrial cracking furnace are investigated to evaluate the effectiveness of the proposed soft sensor method.