Non-convex logarithm embedding subspace weighted graph approach to fault detection with missing measurements

Abstract

In this work, we propose a robust fault detection method to address the problem of increase in missing and/or spurious alarms due to different degrees of loss or corruptions in data. Specifically, given historical data, our aim is to recover a clear low-space representation from corrupted data so that the detection control limits are updated, whenever required. To this end, a novel non-convex logarithm embedding subspace weighted graph detection method is presented. The method compensates the original missing nodes by embedding a non-convex logarithm regularizer, and then constructs an undirected graph model of the compensated nodes. Additionally, the dual constraints of l2,1-norm regularization and specific weights are introduced into the loss function of the graph model to further improve its robustness. Finally, the statistics and detectable criterion of the proposed method are given. Extensive simulations conducted on a real-world hot strip mill process and a multi-phase flow process demonstrate that the proposed method displays more robust detection than other state-of-the-art methods in the presence of outliers and missing measurements.