Bayesian Hierarchical Graph Neural Networks With Uncertainty Feedback for Trustworthy Fault Diagnosis of Industrial Processes.

Deep learning (DL) methods have been widely applied to intelligent fault diagnosis of industrial processes and achieved state-of-the-art performance. However, fault diagnosis with point estimate may provide untrustworthy decisions. Recently, Bayesian inference shows to be a promising approach to trustworthy fault diagnosis by quantifying the uncertainty of the decisions with a DL model. The uncertainty information is not involved in the training process, which does not help the learning of highly uncertain samples and has little effect on improving the fault diagnosis performance. To address this challenge, we propose a Bayesian hierarchical graph neural network (BHGNN) with an uncertainty feedback mechanism, which formulates a trustworthy fault diagnosis on the Bayesian DL (BDL) framework. Specifically, BHGNN captures the epistemic uncertainty and aleatoric uncertainty via a variational dropout approach and utilizes the uncertainty information of each sample to adjust the strength of the temporal consistency (TC) constraint for robust feature learning. Meanwhile, the BHGNN method models the process data as a hierarchical graph (HG) by leveraging the interaction-aware module and physical topology knowledge of the industrial process, which integrates data with domain knowledge to learn fault representation. Moreover, the experiments on a three-phase flow facility (TFF) and secure water treatment (SWaT) show superior and competitive performance in fault diagnosis and verify the trustworthiness of the proposed method.

Noise model based ν-support vector regression with its application to short-term wind speed forecasting.

Support vector regression (SVR) techniques are aimed at discovering a linear or nonlinear structure hidden in sample data. Most existing regression techniques take the assumption that the error distribution is Gaussian. However, it was observed that the noise in some real-world applications, such as wind power forecasting and direction of the arrival estimation problem, does not satisfy Gaussian distribution, but a beta distribution, Laplacian distribution, or other models. In these cases the current regression techniques are not optimal. According to the Bayesian approach, we derive a general loss function and develop a technique of the uniform model of ν-support vector regression for the general noise model (N-SVR). The Augmented Lagrange Multiplier method is introduced to solve N-SVR. Numerical experiments on artificial data sets, UCI data and short-term wind speed prediction are conducted. The results show the effectiveness of the proposed technique.