Large Range Curvature Measurement Based on a Cascaded Hollow-Core Fiber Sensor Combining With a PCA + SVR Demodulation Algorithm

A novel sensor structure composed of a negative curvature hollow-core fiber and a hollow-core fiber is proposed. The highest sensitivity with respect to wavelength reaches 11.21 nm/m<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}^{-{1}}$ </tex-math></inline-formula> in the curvature range from 2.37 to 4.49 m<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}^{-{1}}$ </tex-math></inline-formula>, while that with respect to transmission intensity is 11.01 dB/m<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}^{-{1}}$ </tex-math></inline-formula> in the curvature range from 6.82 to 7.62 m<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}^{-{1}}$ </tex-math></inline-formula>. To expand the curvature measurement range, the support vector regression algorithm is introduced for the prediction of curvature by training and learning the transmission spectra. Combining with the principal component analysis algorithm, which is used for data dimensions reduction, high prediction accuracy can be realized in a large curvature measurement range. The experimental results demonstrate that the mean absolute error and mean squared error for the predicted curvature are as low as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.75\times 10^{-{3}}$ </tex-math></inline-formula> m<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}^{-{1}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.98\times 10^{-{6}}$ </tex-math></inline-formula>, respectively, within the curvature range from 0 to 12.78 m<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}^{-{1}}$ </tex-math></inline-formula>. The prediction time is just 0.223 s to predict all 128 curvatures within the measurement range. Moreover, the prediction efficiency could be further improved, as the high prediction accuracy can be maintained even if the sampling rate of the spectra is reduced.