In this paper, we present a synthesis of the parameters of the fiber Bragg grating (FBG) and the reconstruction of the distributed strain affecting the grating, performed by means of its reflection spectrum. For this purpose, we applied the transition matrix method and the Nelder-Mead nonlinear optimization method. Reconstruction results of the strain profile carried out on the basis of a simulated reflection spectrum as well as measured reflection spectrum of the FBG indicate good agreement with the original strain profile; the profile reconstruction errors are within the single digit percentage range. We can conclude that the Nelder-Mead optimization method combined with the transition matrix method can be used for distributed sensing problems.

This paper presents a simulation study of the simultaneous reconstruction of the non-smooth strain distribution of an optical fiber Bragg grating and its temperature, which is based on the reflection spectrum of the reflected beam of the grating. The transition matrix method was used to model the reflection spectrum of the grating, and the nonlinear Nelder- Mead optimization method was used to simultaneously reconstruct the strain distribution along the grating and its temperature. The results of simulations of simultaneous reconstruction of the strain profile and temperature indicate good accord with the strain profiles and temperature set. The reconstruction errors of the strain profiles are less than 1.2 percent and the temperature change errors are less than 0.2 percent, with a noise level of 5 percent.