In order to deeply exploit intrinsic data feature information hidden among the process data, an improved kernel principal component analysis (KPCA) method is proposed, which is referred to as deep principal component analysis (DePCA). Specifically, motivated by the deep learning strategy, we design a hierarchical statistical model structure to extract multilayer data features, including both the linear and nonlinear principal components. To reduce the computation complexity in nonlinear feature extraction, the feature-samples' selection technique is applied to build the sparse kernel model for DePCA. To integrate the monitoring statistics at each feature layer, Bayesian inference is used to transform the monitoring statistics into fault probabilities, and then, two probability-based DePCA monitoring statistics are constructed by weighting the fault probabilities at all the feature layers. Two case studies involving a simulated nonlinear system and the benchmark Tennessee Eastman process demonstrate the superior fault detection performance of the proposed DePCA method over the traditional KPCA-based methods.

State-of-health (SOH) prediction for lithium-ion batteries is a challenging and important topic in the modern industry. With the advent of cloud-connected devices, there are huge amounts of the battery degradation trend data available. How to make full use of these existing degradation data for the SOH prediction is a valuable problem deserving deep research. Aiming at this problem, a multiple Gaussian process regression (MGPR) method is proposed for the SOH prediction of lithium-ion batteries. In this work, the health indicators (HIs) are firstly extracted from the charging process curves of the batteries, and the mutual information analysis is used to select the important HIs which are strongly correlated to the SOH. These selected HIs are applied as the regression model input for describing the aging procedure of the battery effectively. Then, Gaussian process regression modeling is performed on the different batteries to bring multiple GPR models. Lastly, a weighting strategy based on the prediction uncertainty is designed to integrate the predictions from the multiple GPR models. The method validations are executed on the battery datasets from NASA, and the results show that the proposed MGPR method has higher prediction accuracy than the basic GPR method.

Sensor degradation seriously hinders the practical application of soft sensors. To reduce the negative effect of sensor degradation, in this article, we propose a robust domain adaptation mixture of Gaussian processes (DA-MGP) for online soft sensor modeling of multimode processes. Based on the decomposition of industrial data into a group of Gaussian domains, Gaussian domain discrepancy (GDD) is designed for domain adaptation and process mode recognition. After recognizing the process mode based on GDD, a Gaussian domain adaptation is presented to correct the drifted online input data by domain mapping, which can significantly improve the robustness of the soft sensor against sensor degradation. Furthermore, the domain mapping matrix is utilized as a transferred basis function for a local transferred Gaussian process component, which is used for robust soft sensor modeling. Additionally, an online block processing framework is adopted when the DA-MGP-based soft sensor is applied in online quality prediction. Finally, the TE benchmark process and a real industrial polypropylene process are employed to verify the effectiveness of the proposed method. In the designed five cases of sensor degradation, the DA-MGP-based soft sensor shows its strong robustness against sensor degradation.

Kernel partial least squares (KPLS) is a widely used soft sensor modeling method for nonlinear industrial processes. However, the traditional KPLS is considered as the shallow learning machine and may not capture the vital information hidden among data. In order to exploit the intrinsic data feature information, this paper proposes a deep supervised learning framework based on KPLS, which is referred to as deep KPLS (DeKPLS). Firstly, inspired by deep learning mechanism, a hierarchical feature extraction framework based on KPLS is proposed, where the KPLS is served as the basic feature extraction module. Then, a layer-wise feedforward training strategy is designed for the determination of model architecture. Finally, two actual industrial processes are utilized to demonstrate the effectiveness of the proposed DeKPLS.