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The design of a vibration based fault detection and isolation (FDI) unit that can tackle the combined problem of fault detection, isolation (or identification) and magnitude estimation (collectively known as fault diagnosis), in railway vehicle suspensions is presented. The unit is initially "trained" in a baseline phase based on data obtained from a simplified physics-based model of a railway vehicle suspension. Fault diagnosis is subsequently achieved in an inspection phase through a single, properly preselected, pair of vibration signals acquired from the vehicle, and a recently introduced data-based method, referred to as the functional model based method (FMBM), without resorting to the physics-based model of the baseline phase. The method's cornerstone is the novel class of stochastic ARX-type models capable of accurately representing a system in a faulty state for its continuum of fault magnitudes. Fault diagnosis feasibility in a railway vehicle suspension is demonstrated via Monte Carlo simulations using different types and magnitudes of faults in the physics-based model and generating vibration signals corresponding to the healthy and faulty suspension. Two vibration signals are used by the diagnosis unit: the track velocity profile and the vehicle body acceleration above the trailing airspring. Fault diagnosis based on the FMBM is effective in a compact and unified statistical framework accounting for experimental and modelling uncertainty through appropriate interval estimates and hypothesis testing procedures. The unit is shown to exhibit high sensitivity and accurate estimation of even very small fault magnitudes, to detect and isolate unknown faults for which it has not been trained, and to be robust to high measurement noise, car body mass variations, and varying track irregularity.