Calibration Identifiability and Conditional Design Choices for a Dual-FBG Displacement Sensor

This computational study examines whether a published optical calibration identifies mechanical parameters and supports a unique design recommendation for a dual fiber Bragg grating (FBG) cantilever–spring displacement sensor. Within the adopted series compliance model, the 39.47 pm/mm sensitivity identifies the product of strain transfer and equivalent stiffness. The same anchor admits K = 71.969–91.228 N/m for η = 0.80–1.00. A counterexample extracted from archived nonlinear results shows that η = 0.9500 and 0.9595, with compatible reference stiffnesses of 75.979 and 75.183 N/m, retain only Selected 2 and Selected 3, respectively, across four declared tip geometries under unchanged constraints. Thus, the calibration does not identify a robust choice among the five retained candidates within this family. Selected 2’s nominal 43.07% nonlinearity reduction costs 23.54% more force. Retrospective published optical cycles give a fixed zero root mean square error (RMSE) of 153.6 pm on 37 recovered markers; coordinate and ruler uncertainty preclude hardware accuracy claims. Existing finite element, uncertainty, thermal, bonding and wavelength allocation analyses provide supporting conditional assessments. The contribution is a sensor-specific demonstration of which mechanical and design conclusions remain underdetermined by the adopted calibration. Independent physical validation remains necessary for predictive hardware claims.