Anomaly detection is the identification of abnormal system behavior, in which a model of normality is constructed, with deviations from the model identified as “abnormal”. Complex high-integrity systems typically operate normally for the majority of their service lives, and so examples of abnormal data may be rare in comparison to the amount of available normal data. Anomaly detection is particularly suited for Intelligent Fault diagnosis of such systems since it allows previously-unseen or poorly understood modes of failure to be correctly identified. In this paper, we propose a novel Least Squares Support Vector Machine (LSSVM) based Anomaly Detector for efficiently and accurately detecting imminent faults in complex non-linear systems. The Anomaly Detector is supplemented with a Bayesian Inference Framework in order to allow for a probabilistic interpretation of the classification results. Experiments conducted on data from real test cases discussing crack growth on a planetary gearplate on board a UH-60 BlackHawk Aircraft and bending fan blades aboard a chiller show that the Bayesian LSSVM (B-LSSVM) Anomaly Detector can give high identification rates for both the prescribed ‘unknown’ fault samples and the known fault samples.