Data-Driven Fault Diagnosis Techniques: Non-Linear Directional Residual vs. Machine-Learning-Based Methods

Linear dependence of variables is a commonly used assumption in most diagnostic systems for which many robust methodologies have been developed over the years. In case the system nonlinearities are relevant, fault diagnosis methods, relying on the assumption of linearity, might potentially provide unsatisfactory results in terms of false alarms and missed detections. In recent years, many authors have proposed machine learning (ML) techniques to improve fault diagnosis performance to mitigate this problem. Although very powerful, these techniques require faulty data samples that are representative of any fault scenario. Additionally, ML techniques suffer from issues related to overfitting and unpredictable performance in regions which are not fully explored in the training phase. This paper proposes a non-linear additive model to characterize the non-linear redundancy relationships among the system signals. Using the multivariate adaptive regression splines (MARS) algorithm, these relationships are identified directly from the data. Next, the non-linear redundancy relationships are linearized to derive a local time-dependent fault signature matrix. The faulty sensor can then be isolated by measuring the angular distance between the column vectors of the fault signature matrix and the primary residual vector. A quantitative analysis of fault isolation and fault estimation performance is performed by exploiting real data from multiple flights of a semi-autonomous aircraft, thus allowing a detailed quantitative comparison with state-of-the-art machine-learning-based fault diagnosis algorithms.