You are talking about the turbine air inlet and exhaust ducts not the compressor nozzles. For the compressor nozzles a piping stress analysis would be performed to insure the piping is properly supported and flexible enough as to not impose loads that exceed manufacturers limits. There is no field testing that I know of to prove this only that there will be issues if the loads turn out to be greater than allowables in operation.
For inlet and outlet ducting to the turbine I never did a stress analysis although I imagine if it were round duct a formal computer analysis could be done. Otherwise you could design the duct manually with proper anchors, stops and guides to insure the direction of thermal expansion is away from the connections such that the resulting expansion towards the nozzle is within the limits indicated in the specification. In the cold case the contractor needs to insure the 3/8" alignment is met. I assume you will have expansion joints at the inlet and outlet connections so I guess in the hot case you can check the actual misalignment when in operation to be within the 3/8" and the actual forces during operation you can get if you know the lateral and longitudinal spring constants of the expansion joint which is provided by the manufacturer of the expansion joint, in fact the selection of the expansion joint needs to consider the allowable forces and deflections indicated in the specification. For the axial or longitudinal direction it states the growth of the duct must not exceed 1" back into the expansion joint or in other words in the hot condition the compression of the expansion joint cannot exceed 1" and the load cannot be 200 pounds in that direction axially into the connection. If the expansion joint is placed directly on the nozzle then this means at 1" compression the force cannot exceed 200# or the axial spring constant of the expansion joint cannot exceed 200# per inch. Likewise for a 3/8" lateral deflection when hot the lateral force cannot exceed 200# or the lateral spring constant in any direction needs to be 200#/0.375" or 533.33# per inch.
So knowing expansion joint spring constants in lateral and longitudinal directions you can tell how much force is developed when heated up by measuring the offsets of the expansion joint in the different directions in the hot condition in the field.