Error Characteristics of Neural Network-Assisted Brillouin-Gain-Spectrum-Based Strain Measurements

The frequency shift of the Brillouin gain spectrum (BGS) in optical fibers can be used for strain measurement. However, for the practical application of this BGS-based optical-fiber strain measurement, elucidating the characteristics of its measurement error is crucial. In this study, we first performed numerical simulations to investigate the error characteristics of our proposed neural network (NN)-assisted BGS-based strain measurement method. Notably, strain nonuniformity was considered within the section where BGS was observed (i.e., spatial resolution), and the BGS values within the analysis area, used to measure the strain, were fed into the NN. The results revealed that the error was inversely proportional to the 0.48 and 0.27 powers of the numbers of BGS values in the position and frequency ranges of the analysis area, respectively. Furthermore, the error was inversely proportional to the 0.52 power of the position range and was constant in the frequency range above the maximum frequency variation. Training the NN with BGS values with various full widths at half maximum and noise with different standard deviations enabled it to measure the strain without being affected by them. Furthermore, the strain measurement errors for a beam and ring were investigated through numerical simulations and proof-of-concept experiments. The results confirmed that the proposed method could measure nonuniform strains with V-shaped and sinusoidal variations (typical local strain distributions of beams and rings) with much smaller errors than conventional methods.