Improved lumped modeling approach for FBG temperature sensors addressing nonlinear response and radial gradient effects

Abstract

Fiber Bragg Grating (FBG) sensors are extensively employed in aerospace, energy, and biomedical applications for temperature monitoring, due to their compact form factor, high sensitivity, and multiplexing capability. Conventional lumped thermal models offer acceptable accuracy only under conditions characterized by low Biot numbers (Bi < 0.1), where internal temperature gradients are negligible. However, their predictive accuracy deteriorates in high convective heat transfer environments, such as boiling fluids, molten polymers, or sheathed fibers with large diameters, due to the neglect of radial temperature gradients and nonlinearities arising from temperature-dependent material properties. To overcome these limitations, this study critically examines classical lumped models and proposes equivalent formulations that incorporate nonlinear thermal behavior. Numerical simulations demonstrate that for Biot numbers exceeding 10, conventional models can underpredict core temperature response by as much as 35 % relative to distributed models, whereas the proposed models maintain deviations below 5 %. Notable improvements include the integration of environmental temperature change rates, explicit dependence on the Biot number, and incorporation of temperature-dependent thermal properties. These enhancements reduce core temperature prediction errors by up to 30 % and extend the model's validity across a wide temperature range (20 °C to 800 °C). Consequently, the developed equivalent lumped models offer a computationally efficient and accurate alternative to fully distributed models, facilitating reliable FBG sensor design and improved prediction of thermal response dynamics. © 2026