# Detection and Localization of Multiple Damages through Entropy in Information Theory
## 3 Buried Oil & Gas Pipelines  
Pipelines are defined by four main factors: their external environment (i.e., the boundary conditions), construction material, diameter, and thickness.  
Regarding the external environment, buried pipelines are the prediclected alternative for the distribution of liquid resources over long distances. On the one hand, this is particularly convenient to avoid interferences with other infrastructures, especially in proximity of urbanized areas and potential incidents. Following the terminology in [24], 'incidents' refers in this context to both nonintentional accidents and sabotage or terroristic events. On the other hand, this choice makes visual inspection--which still is the most common practice for scheduled maintenance--unfeasible. This is even more evident for subsea pipelines, which stretch below the seabed inside purposely excavated trenches. Anyhow, even if doable, the length and ramifications of pipeline networks make manade visual inspection generally not cost-efficient. Thus, automated and vibration-based approaches are preferable.  
The reliability of such structural health monitoring (SHM) systems is nevertheless of paramount importance due to the deleterious consequence of damage. This might result in the leakage of pressurized inflammable liquids, with the potential for fire and explosion. The costs in terms of human losses, disruption to the energy supply network, environmental pollution, and other geohazards make the research into advanced solutions economically convenient. Their sensitivity is relevant as well; in high-stress lines, even small cracks can rapidly grow due to the spilling of highly pressurized fluids and lead to abrupt rupture [25].  
For these underground uses, two main categories of pipes are generally employed: \"rigid\" and \"flexible\" pipelines. The former group is made up of the so-called pre-stressed concrete cylinder pipes (PCCP), while the latter one consists of metallic structures. The mechanical behavior is very different in these two options, as in PCCPs the pipe structure carries the structural loads itself, while in steel pipes (SPs) they are supported by the soil-structure interactions, thanks to the steel capability to deflect without breaking.  
This discussion will focus on SPs, since they are overwhelmingly more widespread for oil & gas transportations, both on- and offshore. For the industry needs, oil, gas, and/or pressurized natural gas liquids (NGLs) are moved through these pipelines thanks to compressor (for gas lines) or pump (for oil and NGLs) stations departing from the production regions to distribution centers. In this sense, they represent a much more economically convenient and safer way of transportation than by rail or road [26], with statistics reporting only two deaths and \(11\) injuries on average per year between 1999 and 2001 on US territory, compared to the several thousand involved in truck crashes in the same period [27].  
SPs are generally made in carbon steel due to this material's strength, relatively low weight, and ease of workability. Alloy steels are also applied frequently; alloying elements generally improve mechanical resistance but at a major economic cost, and thus they are reserved for specific uses at extremely high temperatures and pressure. The interested reader is referred to [28] for other relevant aspects about the design and structural analysis of buried flexible steel pipelines.