I find it an excellent question and would be particularly interested in how such an instrumentation compares to our assumptions of how tanks work when they are filled. Sort of a real life validation of our assumptions. My first thought was to use laser scanning but that is much better from the inside and multiple setups around the outside is cumbersome, does not work through insulation and may yield variable results. Strain gauges would work but there would be a zillion of them and as mentioned by others the glue could be a problem. Super accurate volume measurements might work but they'd be an average and would not tell you what each weld seam was doing. Ultrasonics would be mucked up by the product.
Possibly due to lac of imagination, I keep coming back to the idea of strain gauges placed across both vertical and horizontal weld seams, many in the lower half of the bottom course and in the upper half of the top course as well as some in the middle of shell plate and at nozzles / manways, etc, particularly since they would work under the insulation, can be monitored and recorded remotely. You could get several cycles of the tank empty to full, heated to colled off, etc. You'd ahve to monitor setlement since that can affect shell deviations and be cognisant of temprorary events that disturbed the paterns (wind, etc).
It would make a great senior project or masters thesis - which might make it more affordable (??)
