Temperature Compensation of Embedded Fiber Bragg Gratings in Deep-Sea Syntactic Foam Error Bounds and Strain Identifiability

Fiber Bragg gratings (FBGs) embedded in deep-sea syntactic foam are attractive for in situ structural monitoring, but their wavelength response conflates mechanical strain, temperature, and hydrostatic pressure, and the foam remains thermally unequilibrated during deployment. This study develops a quantitative framework for separating these contributions and for allocating the errors that limit mechanical strain interpretation. We report sea-trial measurements from a specimen instrumented with two strain-sensing channels (S1, S2) and two temperature-reference channels (T1, T2), deployed to approximately 4.6 km depth in the Philippine Sea. A two-channel observation model links finite-grating strain transfer, reference-channel mechanical leakage, and spatial temperature mismatch to the compensation error, and is complemented by a coupled thermomechanical–optical validation against the field data. During descent the optical strain indication reached approximately −4.4 × 103 με, and after a four-hour station keeping hold the internal temperature still exceeded the 1.6 °C seawater by 7.7 °C, confirming that thermal transients dominate the residual signal. Nominal thermal correction accounted for 76.7% of the channel-summed station keeping increment and 88.0% of the deck recovery increment—single-deployment, channel-summed point estimates rather than independent replicates. For a 10 με error allocation, the temperature mismatch limit is 0.228 °C under ideal transfer and isolation, tightening to 0.164 °C at a transfer efficiency of 0.8 and weighted leakage of 0.10, and to 0.127 °C with an additional 20 με spatial strain mismatch. The framework converts these observations into quantitative requirements for sensor pairing, calibration stability, and mechanical strain interpretation, and shows that independent thermal information improves mechanical-amplitude identifiability even when the augmented condition number increases.