Inferential modeling has been of significance for modern manufacturing in estimating the quality-related process variables. As an effective inferential model, probabilistic slow feature analysis (PSFA) has gained attention in regression tasks to interpret dynamic properties with a slowness preference. However, PSFA is often challenged by the nonlinear sequential data due to its linear state-space structure. In this article, a new nonlinear extension of PSFA is proposed under the deep learning framework to enhance the dynamic feature extraction with limited labels, incorporating variational inference and Monte Carlo inference to derive the objective function. The proposed model considers the relevance of inputs with outputs as the input weights to upgrade prediction performance. The proposed model is verified through an industrial hydrocracking process to predict diesel yield with missing labels ranged from 0% to 50%, and the root mean squared error is reduced by at least 8.78% compared to PSFA.

Data-driven methods for predicting quality variables in wastewater treatment processes (WWTPs) have mostly ignored the slow time-varying nature of WWTP, and they are data-consuming that need a large amount of independent and homogeneously distributed data, which makes it difficult to collect. To address this issue with few-shot and inconsistent distribution, a transfer learning method called transferable deep slow feature network (TDSFN) for time-series prediction is proposed by leveraging the knowledge of relevant datasets. TDSFN extracts nonlinear slow features of WWTP with inertia from the time series through a deep slow feature network and constructs the domain invariant features based on them. Target feature attention is designed in TDSFN to enhance the predictor adaptability to the target domain by assigning weights to the source features based on their similarity to target features. Furthermore, a variational Bayesian inference framework is introduced to learn the parameters of TDSFN. The effectiveness of TDSFN is verified through prediction experiments based on WWTP.

Since the impressive superior performance demonstrated by deep learning methods is widely used in histopathological image analysis and diagnosis, existing work cannot fully extract the information in the breast cancer images due to the limited high resolution of histopathological images. In this study, we construct a novel intermediate layer structure that fully extracts feature information and name it DMBANet, which can extract as much feature information as possible from the input image by up-dimensioning the intermediate convolutional layers to improve the performance of the network. Furthermore, we employ the depth-separable convolution method on the Spindle Structure by decoupling the intermediate convolutional layers and convolving them separately, to significantly reduce the number of parameters and computation of the Spindle Structure and improve the overall network operation speed. We also design the Spindle Structure as a multi-branch model and add different attention mechanisms to different branches. Spindle Structure can effectively improve the performance of the network, the branches with added attention can extract richer and more focused feature information, and the branch with residual connections can minimize the degradation phenomenon in our network and speed up network optimization. The comprehensive experiment shows the superior performance of DMBANet compared to the state-of-the-art method, achieving about 98% classification accuracy, which is better than existing methods. The code is available at https://github.com/Nagi-Dr/DMBANet-main.