Complexity of Submarine Acoustic Signature

Silent running is a stealth mode of operation for naval submarines. The aim is to evade discovery by passive sonar by eliminating superfluous noise: nonessential systems are shut down, the crew is urged to rest and refrain from making any unnecessary sound, and speed is greatly reduced to minimize propeller noise.

Submarines contain numerous sources of vibration and noise, such as:

  • Diesel engines
  • Generators
  • Auxiliary machinery
  • Drive motor
  • Propeller
  • Exhaust
  • Flow noise
  • Crew

Collectively, all these sources give rise to a characteristic acoustic signature that a submarine radiates. It is important to reduce this signature as much as possible and also to avoid any sudden variations and changes which could lead to its detection.

Measurement and analysis of the noise and vibration environment on board a submarine may be done via accelerometers and hydrophones.

It is important that a submarine has a stealth capability in order to perform many of its intended missions. To achieve the stealth capability, the submarine should minimise the acoustic noise that is broadcast into the water. In addition, it would be beneficial if the presence of the submarine could not be detected by active sonar methods, where a sonar signal is broadcast from another platform and listens to the reflected signals. In some cases, anechoic coatings are used to absorb sound waves from sonar. An example of how complexity allows to classify the various acoustic sources based on the systemic footprint is shown below.

QCM can be used to detect anomalies in the acoustic footprint of a submarine. Anomalies in submarine noise can help enemy submarines or other detection platforms identify their presence. Therefore, it is important to understand how these anomalies are generated and how they contribute to the overall noise signature of a submarine.

Below is an example of complexity analysis of an acoustic signal recording (the light blue curve is a norm of a combination of sound and vibration sources) and of the corresponding standard complexity.

The second chart illustrates the same signal (light blue) but with a new complexity index – the cn2.

The cn2 – one of our new complexity metrics – shows in a clearer fashion the increased complexity of the signal around time step 900. The raw signal doesn’t furnish any indications of this fact. One must remember that complexity doesn’t depend on the actual signal amplitude but on structure-entropy transformations contained therein. The new metric works differently and takes into account also the actual signal amplitude, blending it with entropy and structure. The peak in question clearly points to something in the signal that has momentarily increased its complexity by a substantial amount and the fact should be investigated.

Note that the analysis window is 48 steps, meaning that the blue curves in both charts should be shifted to the left by 48 steps in order to align the time scales. When it comes to detecting submarines, we can have the following attributes:

  • power
  • frequency content
  • signal complexity

Complexity is an interesting and new discriminating factor in that it contains information on the signal’s entropy and structure and on the intensity of entropy – structure transformations. This fact is of immense importance. Structure-entropy transformations are central to many physical phenomena. Treating data from a purely statistical (today the trendy buzzword is “Data Science”) perspective, is a dry numerical exercise poor in terms of physical dimension and depth.


Established originally in 2005 in the USA, Ontonix is a technology company headquartered in Como, Italy. The unusual technology and solutions developed by Ontonix focus on countering what most threatens safety, advanced products, critical infrastructures, or IT network security - the rapid growth of complexity. In 2007 the company received recognition by being selected as Gartner's Cool Vendor. What makes Ontonix different from all those companies and research centers who claim to manage complexity is that we have a complexity metric. This means that we MEASURE complexity. We detect anomalies in complex defense systems without using Machine Learning for one very good reason: our clients don’t have the luxury of multiple examples of failures necessary to teach software to recognize them. We identify anomalies without having seen them before. Sometimes, you must get it right the first and only time!

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