Development of anomaly detection models independent of noise and missing values using graph Laplacian regularization

Anomaly detection is a key technique for maintaining process suitability and safety; however, the quality of process data often deteriorates due to missing or noisy values caused by sensor malfunctions. Such data imperfections may obscure real faults. If anomaly detection models are too sensitive to such abnormal data, they may cause false positives resulting in unnecessary alarms, which may obstruct detection of true process faults. Thus, deterioration of the quality of process data may affect process performance and safety. We propose a new anomaly detection method that utilizes graph Laplacian regularization as a loss function considering data-specific temporal relationships. Graph Laplacian regularization is a mathematical tool used in image processing and denoising to smooth data. We assume that successive process data temporally close to each other have similar values and maintain temporal dependencies among variables. In this study, Laplacian regularization imposes significant penalties when the outputs of neighboring samples lose smoothness, under the assumption that neighboring samples keep similar relationships. Such temporal dependencies can be expressed as a graph structure and extracted with the Nearest Correlation (NC) method. To demonstrate the usefulness of the proposed anomaly detection method, we applied it to an anomaly detection problem in a vinyl acetate monomer (VAM) process. The results show that the model with graph Laplacian regularization achieved higher performance than without graph Laplacian regularization in some fault scenarios. It was confirmed that the proposed method is effective for anomaly detection.