基于BOTDA布里渊背向散射光谱数据的拟合算法

Fitting algorithm for BOTDA Brillouin back scattered-light spectrum data

BOTDA布里渊背向散射光谱数据表现为洛伦兹型曲线,对不同的单模光纤和多模光纤会生成不同的波峰个数,单模光纤中的布里渊背向散射光谱表现为单个波峰,采用非线性最小二乘法对单峰进行拟合,采用高斯-牛顿迭代法求最小二乘解。迭代运算的效率取决于初始值的精度,当误差较大时,迭代次数会增加,甚至无法收敛。采用传统法和定积分法分别获取某一初始值。实验结果表明,在满足同等精度的条件下,定积分法能降低迭代次数,对布里渊背向散射光谱的单峰拟合具有较好的效果。

BOTDA Brillouin back scattered-light spectrum data shows as Lorenz curve, and the curve has different peak numbers when using single mode fiber or multimode fiber, such as the single mode fiber shows one peak. Nonlinear least square algorithm is used to fit the curve, the least-square solution is worked out by Gaussian-Newton method. Algorithm efficiency depends on the initial values, if the initial value has some error, it will increase iteration times, or even the iteration is non convergence. Traditional method and the definite integral method are used to obtain one initial value. Result shows that, in meeting the same conditions of accuracy, the definite integral method can reduce iteration times. This arithmetic is effective to the single peak fitting of the Brillouin back scattered-light spectrum data.