Regularized Wasserstein Distance-Based Joint Distribution Adaptation Approach for Fault Detection Under Variable Working Conditions
Dan Yang, Xin Peng, Cheng Su, Linlin Li, Zhixing Cao, Weimin Zhong
Abstract
Fault detection in the wastewater treatment process (WWTP) has been well addressed when the distributions of training data (source domain) and testing data (target domain) are consistent. However, the distributions may be inconsistent in actual processes due to the variable working conditions caused by the fluctuations in the external environment. Therefore, a joint distribution adaptation (JDA) approach based on the regularized Wasserstein distance (RWD) is proposed to deal with the problem, where RWD is designed based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> norm and kernel density estimation (KDE) probability distribution to precisely measure the difference between the distributions of source and target domains, and then, the label features are also taken into account by using linear discriminant analysis (LDA)-based feature transformation. Not only the input features but also the label features are preserved within the feature space, resulting in a dual advantage for increasing classification accuracy. Therewith, an iterative algorithm based on expectation–maximization (EM) and the generalized conditional gradient (GCG) is designed to solve the problem. Finally, transferable fault detection tasks are constructed in the WWTP. Compared with other methods, the average classification accuracy of the proposed method is improved by 20.9%–108.9%, which validated the effectiveness of our method.