Cyber-attacks on specialized industrial control systems are increasing in frequency and sophistication, which means stronger countermeasures need to be implemented, requiring the designers of the equipment in question to re-evaluate and redefine their methods for actively protecting against advanced mass cyber-attacks. The attacks in question have huge motivations, ranging from corporate espionage to political targets, but in any case, they have a substantial financial impact and severe real-world implications. It should also be said that it is challenging to defend against cyber threats because a single point of entry can be enough to destroy an entire organization or put it out of business. This paper examines threats to the digital security of vibration monitoring systems used in petroleum infrastructure protection services, such as pipelines, pumps, and tank farms, where malicious interventions can cause explosions, fires, or toxic releases, with incalculable economic and environmental consequences. Specifically, a deep spiking neural network anomaly detection method is presented, which models the spike sequences and the internal presentation mechanisms of the information to discover with very high accuracy anomalies in vibration analysis systems used in oil infrastructure protection services. This is achieved by simulating the complex structures of the human brain and the way neural information is processed and transmitted. This work uses a particularly innovative form of the Galves–Löcherbach Spiking Model (GLSM) [1], which is a spiking neural network model with intrinsic stochasticity, ideal for modeling complex spatiotemporal situations, which is enhanced with possibilities of exploiting confidence intervals by modeling optimally stochastic variable-length memory chains that have a finite state space.