This study proposes a real-time scour warning system of railway bridges by means of a remote ambient vibration monitoring as an alternative method for the impact test. The real-time scour warning system consists of an edge computing system, wireless communication and cloud computing. The monitored ambient vibration signals are processed and the target frequency is identified in the edge computing system, and the identified frequencies are sent to a cloud computing system via Wi-Fi. In the cloud computing, possibility of scour is estimated and send out warnings as needed. A stochastic approach is investigated for the real-time scour warning because of relatively poor signal to noise of the ambient vibration signals comparing to that from the impact test. It is also investigated what kind of probability distribution best represents the observed frequencies. The stable distribution showed the best fit to the observed frequency distributions. Observations demonstrated an extremely low probability of scour of the target bridge during swollen river water period.