Time Domain Reflectometry
TDR is the process of taking a fibre-optic cable, shining a light down it, and being able to tell where problems are, even before the cable is broken. All the equipment needed is an oscilloscope, a fast photodiode and a fast light source.
Fibre optic cable works due to internal reflection. This is due to the glass/glass interface and the glass/air interface beyond it. Sharply bent cable in water will not work as effectively as the same bend in air.
The speed of light in the cable is known very accurately, so the time it takes for the laser pulse to scatter back from the fault tells us the distance down the line to the fault. Faults can be shearing of the cable, right down to an unusually sharp bend in it. The faster the pulse (on-off) and the better the detector, the more accurately the fault can be detected. For our needs, within 5 metres is fine, due to this cutting it down to just five cells in a row. Resolution of >10mm is the state of the art. The trace from the oscilloscope shows each bend as a return against time.
This allows us to sense changes to the outside of the fibre due to external changes. For example, due to the sensitivity of this technique, the presence of carbon dioxide or water vapour can be detected by the change in density, and hence refractive index, of the atmosphere surrounding the bend. The detection of the immersion of a bend in water is a trivial matter.
Long term degradation of the cable would occur due to seawater attacking the glass of the fibre, but it would, I believe, be many years before this was a major problem. At that time, a second cable, with a more logical path, would be run under the surface by divers.
The only forseeable problem is that the cable could be easily broken. This could be reduced by leaving a small amount of slack cable and supporting it on the structure to keep it mostly out of the water, away from marine organisms and animals, and drifting debris (However, floating debris could not get under the mat of cells except in storm conditions, and even then would be trapped near the edges.)
This would result in a smart, stress and strain monitoring system, providing valuable realtime warnings and data for the building of subsequent floating cities.