Mobile networks are universally used for personal communications, but also increasingly used in the Internet of Things and machine-to-machine applications in order to access and control critical services. However, they are particularly vulnerable to signaling storms, triggered by malfunctioning applications, malware or malicious behavior, which can cause disruption in the access to the infrastructure. Such storms differ from conventional denial of service attacks, since they overload the control plane rather than the data plane, rendering traditional detection techniques ineffective. Thus, in this paper we describe the manner in which storms happen and their causes, and propose a detection framework that utilizes traffic measurements and key performance indicators to identify in real-time misbehaving mobile devices. The detection algorithm is based on the random neural network which is a probabilistic computational model with efficient learning algorithms. Simulation results are provided to illustrate the effectiveness of the proposed scheme.